Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x + 2$ and $ JT = 4x + 22$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x + 2} = {4x + 22}$ Solve for $x$ $ 5x = 20$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({4}) + 2$ $ JT = 4({4}) + 22$ $ CJ = 36 + 2$ $ JT = 16 + 22$ $ CJ = 38$ $ JT = 38$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {38} + {38}$ $ CT = 76$